Combinatorial quantification of distinct neural projections from retrograde tracing

Comprehensive quantification of neuronal architectures underlying anatomical brain connectivity remains challenging. We introduce a method to identify the distinct axonal projection patterns from a source to a set of target regions and the count of neurons with each pattern. For a source region projecting to n targets, there are 2 - 1 theoretically possible projection types, although only a subset of these types typically exists. By injecting uniquely labeled retrograde tracers in k regions (k < n), one can experimentally count the cells expressing different combinations of colors in the source region^1,2. Such an experiment can be performed for n choose k combinations. The counts of cells with different color combinations from all experiments provide constraints for a system of equations that include 2 - 1 unknown variables, each corresponding to the count of neurons for a projection pattern. Evolutionary algorithms prove to be effective at solving the resultant system of equations, thus allowing the determination of the counts of neurons with each of the possible projection patterns. Numerical analysis of simulated 4 choose 3 retrograde injection experiments using surrogate data demonstrates reliable and precise count estimates for all projection neuron types. We illustrate the experimental application of this framework by quantifying the projections of mouse primary motor cortex to four prominent targets: the primary and secondary somatosensory and motor cortices.